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Optical Interferometers
E N CYC LO PE D IA O F A S T R O N O MY AN D A S T R O PHYS I C S Optical Interferometers
Optical INTERFEROMETERS are astronomical instrumentsdesigned to provide higher angular resolving power thanis possible with a conventional optical telescope or, inother words, the capacity to measure smaller angles andto discern finer details in an image.
The ability of a telescope to resolve fine detail in an astronomical object is fundamentally limited by thewavelength (color) of the light used for the observationsand the diameter of the mirror or lens that collects light imposes a limit on the resolution achievable unless specialtechniques are used, but even above the atmosphere theonly way to see finer detail with a telescope would be toobserve at a shorter wavelength (bluer light) or to build a The measurement of the sizes of stars was the challenge that led to the development of optical Figure 1. The angular diameter of a star θ and the angular
interferometry. The size of a star cannot be measured separation θs of the components of a binary, or double star.
directly but, if its angular size θ and its distance D canbe determined, its diameter d can be calculated from d = D × θ , as illustrated in figure 1. From abovethe Earth’s atmosphere the images of all but a very fewstars appear as points of light blurred only by the wavenature of light. From the ground, turbulence in the Earth’s atmosphere corrupts the light from a star and blurs itsimage so badly that no star, other than our own Sun, canhave its size determined from its image. Astronomers callthis blurring effect ‘SEEING’.
FIZEAU (1868) was the first to propose an interferomet- ric method to overcome the effects of seeing. He noticedthat when a star was viewed through a small aperture itsimage was blurred but was otherwise regular in shape—unlike that from a large telescope where the image is blurred but also continually changing. This led him tothe idea of putting a mask with two small holes in frontof a telescope and observing the superimposed images of the star. The combined image would be crossed by inter-ference fringes—alternate bright and dark bands. Fizeau Figure 2. Cross section of the Michelson stellar interferometer
realized that the contrast of the fringes, the difference in mounted on the 100 inch Hooker telescope on Mount Wilson in brightness of the bright and dark bands, would diminish as the separation of the apertures was increased, and thatthe fringes would vanish at a separation directly related tothe angular size of the star. Stephan (1873) tested Fizeau’s Mount Wilson in California was too small to observe idea but was unable to observe the disappearance of the the disappearance of the fringes, Michelson had the fringes since the largest telescope available had an aperture brilliant idea of attaching a long beam across the front diameter of only 0.8 m, which was too small. Nevertheless, of the telescope to carry mirrors to relay starlight from Fizeau’s idea is the basis of modern optical interferometers separations greater than the telescope aperture into the which, by measuring the fringe contrast as a function of telescope. A diagram of Michelson’s stellar interferometer the separation of the apertures, are able to determine the angular sizes of stars and the angular separations of close In the absence of a turbulent atmosphere even the binary (double) stars as illustrated in figure 1.
largest optical telescopes, with aperture diameters of 8– The first measurement of the angular diameter 10 m, would only reveal about a dozen stars as images of a star was by MICHELSON and PEASE in 1920 when whose sizes could be measured. While interferometric they measured the angular diameter of Betelgeuse, the techniques, like speckle interferometry and developments bright red supergiant star in the constellation of Orion.
of the masking interferometry originally proposed by Because even the 100 inch (2.5 m) Hooker telescope on Fizeau, have enabled telescopes to measure stars to the Copyright Nature Publishing Group 2001Brunel Road, Houndmills, Basingstoke, Hampshire, RG21 6XS, UK Registered No. 785998and Institute of Physics Publishing 2001Dirac House, Temple Back, Bristol, BS1 6BE, UK Optical Interferometers
E N CYC LO PE D IA O F A S T R O N O MY AN D A S T R O PHYS I C S limits set by their aperture diameters and the wavelength of light, interferometry has moved on to combine the light from separate apertures in order to increase the technology in the form of laser metrology, adaptive optics, fast electronics and computer control and, sincethe driving force was primarily the measurement of stars and binary stars, most instruments have been calledstellar interferometers.
capabilities of interferometers offer other possibilitiesthat are exciting astronomers and astrophysicists as the potential of interferometry is recognized.
example, these include the determination of accuratestellar positions (ASTROMETRY), the search for EXOPLANETS(planets other than those in the solar system) and the Figure 3. The variation of correlation with baseline for two
single stars whose angular diameters are shown in the figure.
measurement of the sizes of cores of ACTIVE GALAXIES.
The oscillating curve is the response for a binary star. Theprimary star of the binary has an angular diameter of 1 mas and Basic theory
is twice as bright as the secondary. The angular separation of the The minimum angle θmin resolvable by a circular aperture of diameter d at a wavelength λ is given by intensity distribution () of the source can be found.
The fringe phase φ12(0), as a function of the aperture separation, provides information on asymmetries in the 500 nm. The angular diameters of all but a few stars are angular intensity distribution—for a symmetrical source less than a very few milliarcsec (mas) and interferometers the fringe phase will be zero or 180◦ for all aperture with aperture separations (baselines) in excess of 10 m are In practice, the Earth’s turbulent atmosphere disrupts The combination of the light from two separate the phase and, for observations made with a single apertures is similar to a Young’s double-slit experiment baseline at a time, only the degree of coherence |γ12(0)| is with interference fringes being formed in the combined measurable. In the absence of the phase, departures from images of the source. A measure of the contrast of the symmetry in the intensity distribution cannot be detected.
fringes is Michelson’s fringe visibility V defined as Thus, measurements with a single baseline yield only thevisibility, and these are interpreted as the angular size of an equivalent strip source or the angular diameter of a radially symmetrical disk source. To obtain images it isnecessary to measure both the modulus and phase for at where Imax and Imin represent the maximum and minimum least three baselines simultaneously.
In practice, many interferometers measure the square A more sophisticated approach involves considera- of the fringe visibility, which is usually called the tion of the coherence of the light at the two apertures. Thecomplex degree of coherence γ terms of a modulus |γ12(τ )| and a phase φ12(τ ), where τ is the difference in arrival time of the two beams at the point 12(τ ) = [V12(τ )]2 = |γ12(τ )|2. of combination and the subscripts 1 and 2 represent the As an example of the variation of correlation with baseline figure 3 shows the relationships for two stars with different angular diameters, both assumed to be 12(τ ) = |γ12(τ )| exp[iφ12(τ )]. uniformly bright across their circular disks. Also shown is When the intensities from the two apertures are equal, the fringe visibility V12(0) = |γ12(0)|. The complex degree of If there is a path difference between the beams in an spatial coherence γ12(0) (i.e. with τ = 0) and the angular interferometer at the point where they are combined there distribution of intensity across the source are a Fourier will be a loss in fringe visibility and in correlation. The transform pair—the van Cittert–Zernike theorem.
magnitude of the loss depends on the spectral bandwidth used for the measurements. The wider the bandwidth, the greater the loss. The reduction in correlation can be expressed in terms of the coherence length of the light If |γ12(0)| and φ12(0) are measured over an appropriate l = λ2/ λ, where λ is the spectral range of baseline lengths and orientations, the angular bandwidth and λ is the mean wavelength.
Copyright Nature Publishing Group 2001Brunel Road, Houndmills, Basingstoke, Hampshire, RG21 6XS, UK Registered No. 785998and Institute of Physics Publishing 2001Dirac House, Temple Back, Bristol, BS1 6BE, UK Optical Interferometers
E N CYC LO PE D IA O F A S T R O N O MY AN D A S T R O PHYS I C S The Fourier transform of the intensity distribution across the spectral bandpass is the complex degree ofcoherence and, as an example, the correlation for a flat-topped spectral bandpass is given by C12( OPL) = [V12( OPL)]2 = sin x where x = π OPL/ l and OPL is the optical path length difference between the beams (optical path length is the product of the geometrical path length in a medium andthe refractive index of the medium).
In order to obtain accurate measurements of fringe visibility or correlation, the optical paths from the source to the point of combination of the beams must be equal towithin a small fraction of the coherence length ( OPL Overcoming the effects of atmospheric turbulence
The effect of atmospheric turbulence on incoming light
is to distort the shapes of wavefronts and introduce
randomly varying phase shifts, wavefront tilts, and
Figure 4. A simplified layout for a long-baseline optical
wavefront curvatures. The significance of these effects interferometer illustrating the main features. A represents the for interferometry depends on the observing wavelength.
input apertures and T the wavefront tip-tilt correcting mirrors, The spatial scale of the wavefront distortions is measured is the difference in path length for the two beams of starlight at the input apertures, C is the path-equalizing carriage, B is the beam-combiner and d is the baseline of the interferometer.
a wavefront over which the phase fluctuations have an Further details are discussed in the text.
rms value of one radian. The temporal scale of the phasefluctuations is represented by t0, the time interval at theend of which the rms value of the phase fluctuations is at the input apertures and an internal variable optical delay must be incorporated in the instrument to equalize the Both r0 and t0 vary as λ6/5 so both improve for longer optical path lengths at the point of beam combination. One wavelengths. Observed values depend on the site, and method of achieving this is shown in figure 4.
both vary from night to night and during the course of eachnight. Typical values for the visual region of the spectrum For interferometers in which the light from only two apertures at a time can be combined, only the In order to overcome the effects of atmospheric fringe visibility or the correlation is measurable since turbulence most optical and infrared interferometers use the phase is disrupted by the atmosphere.
apertures of diameter less than r0 and signal sampling measurements, made with only a single baseline at a time, times less than t0. In addition, tilts in the sections of the the Fourier transform yields the intensity distribution wavefront accepted by the apertures of an interferometer for the equivalent strip source (i.e. the source intensity are individually measured and corrected in real time by distribution reduced to the equivalent strip source parallel tip-tilt mirrors (first-order ADAPTIVE OPTICS). This ensures to the baseline direction). No information on asymmetries that the beams from the apertures are combined optimally in the intensity distribution across the source can be for the measurement of the interference fringe contrast.
derived and true images cannot be constructed.
In principle, instrumental loses and residual seeing angular diameter determinations and studies of binary effects are calibrated by observing unresolved stars systems this is generally of no concern—the relative between observations of the star or object to be measured.
brightnesses of the components of a binary system can be Two-aperture interferometers
determined but with a 180◦ ambiguity in the orientation Modern optical/infrared interferometers operate with baselines ranging from a few metres up to a few hundred diameters with complementary measurements made with conventional telescopes enables fundamental stellar INTERFEROMETRY: GROUND). This necessitates mounting the input apertures on separate structures properties such as surface fluxes, effective temperatures, anchored to the ground. Because of the short wavelengths radii and luminosities to be determined. For many binary involved, extremely good stability and freedom from stars radial velocities can be determined spectroscopically.
vibration is essential. With the input apertures at fixed For such systems stellar masses and distances can also be locations the arrival time of the light from a star will differ Copyright Nature Publishing Group 2001Brunel Road, Houndmills, Basingstoke, Hampshire, RG21 6XS, UK Registered No. 785998and Institute of Physics Publishing 2001Dirac House, Temple Back, Bristol, BS1 6BE, UK Optical Interferometers
E N CYC LO PE D IA O F A S T R O N O MY AN D A S T R O PHYS I C S Table 1. Interferometers and interferometric arrays.
Sydney University Stellar Interferometer (SUSI) Prototype Interf´erom`etre `a 2 T´elescopes (I2T) Grand Interf´erom`etre `a 2 T´elescopes (GI2T) Sydney University Stellar Interferometer (SUSI) Infrared–Optical Telescope Array (IOTA) Cambridge Optical Aperture Synthesis Telescope (COAST) Navy Prototype Optical Interferometer (NPOI) (Astrometry) Center for High Angular Resolution Astronomy Array Very Large Telescope Interferometer (VLTI) † Key: C = program completed and instrument shutdown; W = instrument working; UC = undergoing commissioning orunder construction.
Multiple-aperture interferometers
In order to form images with an interferometer it is either an array of apertures, from which the two to necessary to use more than two apertures simultaneously.
be used can be selected, or there is the possibility of For each pair of apertures in an imaging array the same moving input optics between stations to provide a range of constraints must be met as for a single-baseline instrument.
baselines. Instruments listed with three or more apertures This includes matching the optical paths to within a small are generally intended to combine the light from several, fraction of the coherence length, dealing with the effects or all, of the apertures simultaneously for the construction of wavefront distortion, and using rapid signal sampling to limit phase smearing during each observational sample Interferometers and interferometric arrays intended for astrometric measurements are similar in principle to Even though the phase measurement for a single other interferometers and arrays, but differ in having ex- baseline is corrupted by the atmosphere, it is possible tensive monitoring of the instrument stability by laser to determine a ‘closure phase’, free of corruption, for metrology and an optical delay compensator operatingin vacuum. Astrometric interferometers are of two broad each independent triangle of baselines formed by three types—global and narrow-angle (differential). Global as- apertures of an array. Aclosure phase is solely a function of trometric interferometers, such as the NPOI Astrometric the fringe phases due to the source since, in the calculation Array in Arizona, measure the relative positions of stars of the closure phase, the atmospherically induced phase over the whole sky with the aim of maintaining the Hippar- cos frame and improving proper motion determinations of the angular intensity distribution across the source by extending the timebase of measurements. Narrow- and, together with the fringe visibilities measured for the angle interferometers are effectively double interferome- baselines, enable an image of the source to be constructed.
ters with each interferometer linked to the other by preci- This technique, first developed for radio wavelengths, has sion laser metrology. One interferometer is phase locked been adapted to optical and infrared wavelengths.
to a reference source while the second is locked to the tar- Multiple-aperture interferometric arrays are aimed at get source to search for relative motion produced by a faint imaging a range of astronomical phenomena including the unseen companion such as a brown dwarf or planet.
birth of stars and planetary systems, close binary systems An alternative interferometric technique for the and the cores of active galaxies and quasars.
detection of exoplanets is the nulling interferometer. Byworking in the infrared, and suppressing the stellar flux Modern optical interferometers
by combining the star’s light out of phase, it should be Table 1 contains a list of optical/infrared interferometers possible to detect planets down to Earth size but with an and interferometric arrays with the acronyms by which they are generally known. The instruments shown as Figure 5 shows an aerial view of SUSI, which is located having two apertures combine the light from only two in northern New South Wales in Australia. SUSI has the Copyright Nature Publishing Group 2001Brunel Road, Houndmills, Basingstoke, Hampshire, RG21 6XS, UK Registered No. 785998and Institute of Physics Publishing 2001Dirac House, Temple Back, Bristol, BS1 6BE, UK Optical Interferometers
E N CYC LO PE D IA O F A S T R O N O MY AN D A S T R O PHYS I C S is presented in Science with the VLT Interferometered F Paresce (Berlin: Springer, 1997).
Figure 5. The Sydney University Stellar Interferometer (SUSI)
seen from the northern end of its 640 m long baseline array.
distinction of having the longest baseline array of anyoptical/infrared interferometer. Since it can only observewith two apertures at a time it does not form images.
Instruments such as NPOI, the CHARA Array on MountWilson in California, and COAST in England all havearrays of input apertures arranged along three arms likethe letter Y in order to form images by combining the lightfrom three or more apertures simultaneously. The Keckinterferometer and ESO’s VLTI will combine the light fromseparate 8–10 m class telescopes for imaging of fainterobjects.
Optical and infrared interferometry and interferomet- ric imaging is in its infancy but promises to make signifi-cant contributions to astrophysical research in the 21st cen-tury.
An overview of optical interferometry and its potential for astrophysics, as presented at a NATO Advanced StudyInstitute written by authors expert in various aspects of thefield is contained in High Angular Resolution in Astrophysicsed A-M Lagrange, D Mourard and P L´ena (Dordrecht:Kluwer, 1997).
A large proportion of reports on the developments in optical and infrared interferometry is contained in theproceedings of international symposia and workshops.
However, the key technical papers in the developmentof optical interferometry have been collected in SelectedPapers on Long Baseline Stellar Interferometry SPIE MilestoneSeries, Volume MS 139, ed P R Lawson (Bellingham, WA:SPIE, 1997).
The theory of interference with partially coherent light is treated comprehensively by Born M and Wolf E1975 Principles of Optics: Propagation, Interference, and Diffraction of Light 5th edn(Elmsford, NY: Pergamon).
A review of the scientific potential, particularly for interferometric arrays involving large aperture telescopes, Copyright Nature Publishing Group 2001Brunel Road, Houndmills, Basingstoke, Hampshire, RG21 6XS, UK Registered No. 785998and Institute of Physics Publishing 2001Dirac House, Temple Back, Bristol, BS1 6BE, UK

Source: http://www.mao.kiev.ua/lectures/Optical_Interferometry/Additional_reading/2906_Optical_Interferometers.pdf

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